Thus {{ppp|p={{{1}}}|a=fa|b=fb|..}} can represent any function f given by a set of pairs (a,fa), (b,fb), .. , except that these cannot include a pair (p,fp). To allow the latter also, we can use {{ppp|p=q{{{1}}}|qa=fa|qb=fb|..}}.

Similarly, with Template:Pp we can allow a pair (1,f1) if we use {{pp|q{{{1}}}|qa=fa|qb=fb|..}}, etc. If {{{1}}} takes integer values with a lower bound we can also apply a shift, see that template.